ART OF PROGRAMMING

Let us consider a simple BASIC program which checks marks of each student and count the number of students passed. Using this program, we will try to learn the nuance of this art .

A program is made of three fundamental components namely 1. sequential flow 2. conditional flow, 3. repetitive flow.

1. Statements from line 10 to 40 are just flowing sequentially. Line 10 is just a title. Rem means remark. 20 initiates a counter. Pass marks is fixed in 30. In line 40, N stores number of students. These statements are executed one by one.

2. Line no. 50 to 80 is executed repeatedly. That is, the statements 60 and 70 is executed 10 times since N =10. Each time the control comes to line 60, it READs a value from DATA statement (line 90) and store it in "MARK".

3. When the control comes to line 70, it makes a decision. If the mark is equal to or greater than pass mark, the count is increased by 1. If the condition is not met, the control just goes to 90- next mark. So the "if" statement is also called branching statement.

Line 100 output the result.

Mainly using these three components, any complicated program can be built. No coding is possible without them.

Other points to ponder:
Count, passmark are names of storage (Memory) in which relevant values are stored.
The statements between FOR and NEXT is repeatedly executed N times.
Count = count + 1 means 1 is added to the old value of "count" and the new value replaces the old one.

A program is snapshot of working of an engine. It is the action frozen in codes. It is like a sport's still photo. When the program is fed into the computer, it comes to life. It takes inputs, process them and gives output.
Programming is the new age skill that everybody should learn. It is creative, entertaining and solves problems.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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